Lattice dynamics and dielectric properties of incipient ferroelectricTiO2rutile

The phonon frequencies at the Γ point, the Born effective charges, and the dielectric permittivity tensors of ${\mathrm{TiO}}_2$ rutile are calculated using the variational density-functional perturbation theory. The calculated phonon frequencies agree with experiment within a few percent. We analyze the corresponding theoretical eigenvectors as well as the interaction of the vibration modes with the electric field. The Born effective charges of ${\mathrm{TiO}}_2$ rutile are much larger than the nominal charges of ${\mathrm{Ti}}^{4+}$ and ${\mathrm{O}}^{2\mathrm{-}}$ ions, as well as those of ${\mathrm{SiO}}_2$ stishovite despite the structural similarity. A giant LO-TO splitting is observed for ${\mathit{E}}_{\mathit{u}}$ and ${\mathit{A}}_{2\mathit{u}}$ modes. The O ions in rutile as well as in stishovite are found to have a counterintuitive reversed electronic polarization near the nuclei. The calculated large, anisotropic static dielectric permittivity tensors as well as electronic dielectric permittivity tensors also compare favorably with experiments.